Effect of stability of X-ray pulsar profiles on range measurement accuracy in X-ray pulsar navigation

The Crab pulsar is an isolated rotation-powered pulsar which emits large X-ray fluxes, making it a candidate source for carrying out the X-ray pulsar navigation (XNAV). The long-term stable profiles are considered as the foundation of XNAV. However, systematic studies of the long-term stability of the X-ray pulsar profile and its effect on range accuracy in XNAV are lacking. In this paper, we use the X-ray band (2–16 keV) data monitored by Rossi X-ray timing explorer (RXTE) spacecraft over the latest 11 years, to first investigate the stability of the Crab pulsar including the profiles after the glitches. Furthermore, some measurements of the long-term profile shape, including Pearson correlation coefficient, standard deviation and spectral entropy, are presented both in the time domain and in the frequency domain. In the data processing, the Fourier analysis and cross-correlation are used to deal with the 191 RXTE data sets. With the help of the Cramer-Rao theory, the effect of the profile variation on the error of the range determination in XNAV is studied. Furthermore, after analyzing those errors, the effect of the stability of the Crab pulsar on range determination is confined to more narrow limits. The results demonstrate that the 2–16 keV profiles are almost constant during the period 2001–2012. The profiles after the glitches show no significant discrepancy. The variation of Crab profile inevitably has an influence on the navigation precision to a certain extent. The calculated range error along the pulsar line-of-sight due to the stability of the pulsar profile is 34 m±25 m.